Kapur, after a 66 on first day, is now five-under 139 and in tied 29th place after being tied fifth overnight.
Others making the cut were Arjun Atwal (73-67) in tied 35th place, Jyoti Randhawa (71-70) and Anirban Lahiri (69-72) are tied 48th and SSP Chowrasia (71-71) was tied 64th.
The Indians who missed the cut were Gaganjeet Bhullar (74-70), Rahil Gangjee (74-70) in tied 94th, Rashid Khan (74-72) in tied 108th and Jeev Milkha Singh (73-74) in tied 120th.
Meanwhile, the Spanish star Miguel Angel Jimenez moved into the lead after the second round.
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The charismatic veteran, who is the oldest player in the field, was once again in his element as he raced atop the leaderboard with a 66 at 11-under, even as Thailand's Kiradech Aphibarnrat fired his way back into contention with five-under-par 67 to pile the pressure from second place at 10-under.
Thongchai Jaidee of Thailand also made his move by carding a similar 66 to share third place with Australia's Scott Hend and one-time Asian Tour winner, Richard T Lee of Canada at nine-under.
After missing the cut at the season-opening event in Malaysia last week, Kiradech returned with all guns blazing at the richest golf tournament in Thailand.
The 2013 Asian Tour Order of Merit champion, who started on the back-nine 10, had an opening birdie to get his round going. He went on to mix two bogeys against two birdies for an outward 35. But it was an eagle-three on the second hole that surged him further up the leaderboard.
Crowd favourite Thongchai did not disappoint the galleries as he improved on his opening 69 with 66 that was highlighted by seven birdies and one bogey.